The Ring is retarded to 0 rad/s

Consider a ring of mass \(m\) and radius \(R\) touching a rough wall of coefficient of friction \(\mu\) as shown in figure. The ring has an initial angular velocity of \(\omega_0\).

Find the time taken by the ring to come to a halt.

Details and Assumptions

  • The ring doesn't translate on the wall.

  • \(\mu = \dfrac{1}{\sqrt{3}} \)

  • \(m = 1 kg\)

  • \(R = 1 m\)

  • \(\alpha = \dfrac{\pi}{3}\)

  • \(\omega_0 = 10 rad/s\)

  • \(g = 10 m/s^2 \)

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